Global Positioning System GPS

							Global Positioning Systems
          (GPS)
  for Precision Farming

       An Introduction
                     The plan
• Introduction to GPS
  –   What is GPS
  –   How GPS works
  –   Differential Correction
  –   Integration and application of GPS into PF
      systems
         Introduction to GPS
• What is GPS
  – The Global Positioning System (GPS) is a
    worldwide radio-navigation system formed from a
    constellation of 24 satellites and their ground
    stations
  – GPS receivers use these satellites as reference
    points to calculate positions and time
  – Originally known as NAVigation System with
    Timing And Ranging (NAVSTAR)
How GPS Works (Six Steps)
1.   Triangulation
2.   Distance
3.   Clocks
4.   Satellite Position
5.   Coordinate system
6.   Errors
                  Triangulation
• Number of Satellites
  –   One distance = sphere
  –   Two distances = circle
  –   Three distances = two points
  –   Four distances = one point
  –   Three distances + earths surface = one point
• Locking
  – 1,2 satellites - No lock, course time
  – 3 Satellites - 2D positioning (Earth’s surface assumed)
  – 4 Satellites - 3D positioning (Lat/Lon/Alt)
   Triangulation - critical points
• Position is calculated from distance
  measurements (ranges) to satellites.
• Mathematically we need four satellite ranges
  to determine exact position.
• Three ranges are enough if we reject
  ridiculous answers or use other tricks.
• Another range is required for calculation of
  time.
                  Distance
• Distance = Speed x Time ?
  – 180 miles = 60 miles per hour x 3 hours
• Speed of radio waves ?
  – 186 kmps
• Time
  – 0.06 second
• Distance = 186000 mps x 0.06 s
  – D = 11,160 miles (11Hr 58 Min period)
• Accuracy (+/- 0.000,000,001 sec) = +/- 1 ns
                     Distance
• How does a receiver time the signal travel?
  – Satellites send a pseudo-random code
     • (each sends its own song of 1’s and 0’s)
  – Receiver matches its calculated sequence with the
    received signal by delaying more or less it’s signal
  – The amount of delay = the transit time!
• How does the receiver separate the signals of
  each of the satellites?
  – Each satellite has it’s own sequence (song)
    calculated through a formula
  – Formula is conveyed in data from the satellites
    Distance - critical points
– Distance to satellites is determined by measuring
  signal travel time.
– Assume satellite and GPS receiver generate same
  pseudo-random codes at the same time.
– By synchronizing the pseudo-random codes, the
  delay in receiving the code can be found.
– Multiply delay time by the speed of light to get
  distance
               Synchronization
• Satellites timing is extremely accurate.
   – precise atomic clocks on board.
• All satellite clocks are synchronized and they
  send their codes at a known time
• Ground GPS unit synchronizes its clock with
  the satellites
   – Four satellites with same time = only one correct
     solution for 1. time and 3. distances
      • (4 Equations, 4 unknowns)
  Synchronization - critical points
• Accurate timing allows distance to satellites to
  be measured
• Satellites achieve accurate timing with on-
  board atomic clocks.
• Receiver clocks can be accurate because an
  extra satellite range measurement can
  remove errors.
      Where are the satellites?
           (ephemeris)
• Satellites are launched into precise orbits
• GPS receivers use an almanac to calculate
  accurate positions for the satellites
  (ephemeris)
• Almanac is sent from satellites
• US Airforce measures error in ephemeris
  (satellite position and speed) when they fly
  over C. Springs
• Corrected ephemeris info is sent up to the
  satellite
     ephemeris - critical points
• Satellite position (ephemeris) must be known
  as a reference for range measurements.
• GPS satellite orbits are very predictable.
• Minor variations in their orbits are measured
  by the Department of Defense.
• The ephemeris error information is sent to the
  satellites, to be transmitted along with the
  timing signals.
          Coordinate Systems
• ECEF Coordinates
  – Latitude/Longitude/Altitude
     • Degrees Minutes Seconds (Ag Hall, OSU USA)
        – Latitude 360 07’ 29” N
        – Longitude 970 04’ 21” W
  – Latitude = degrees from equator N or S
  – Longitude = degrees from Greenwitch E or W
  – Altitude = Meters above reference geoid
     • GPS uses WGS84 Ellipsoid (ECEF)
  – Can be transformed to others: NAD27, NAD83
• See: Peter Dana’s Web site
            Coordinate Systems
• UTM
  –   Cartesian positioning in meters
  –   Abbreviation for “Universal Transverse Mercator”
  –   Divided into cartesian zones
  –   60 wide, 840 North to 800 south
• Reference
  – Specifies a starting point for measurement
  – eg.: (NAD 1927)
  – Important to account for error between survey
    reference and actual lat/lon
Computation of distance along
         Longitude

                          S =R
                             Lon

        R=6,433,000m
                           S      Lon



                             R

          31.2 m/s




                     South
Computation of distance along
          Latitude

                      SLat=R40
             R40          

       R40=R cos 
          25.6 m/s




                     South
               Error Budget
Typical Error in Meters (per satellite)
                   Standard GPS Differential GPS
Satellite Clocks        1.5                 0
Orbit Errors            2.5                 0
Ionosphere               5                 0.4
Troposphere             0.5                0.2
Receiver Noise          0.3                0.3
Multipath               0.6                0.6
SA                      30                  0

Typical Position Accuracy
Horizontal               50                1.3
Vertical                 78                 2
3-D                      93                2.8
                                   Trimble Navigation Limited